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Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression
Zhaozhi Qian · William Zame · Lucas Fleuren · Paul Elbers · Mihaela van der Schaar

Wed Dec 08 12:30 AM -- 02:00 AM (PST) @ Virtual

Modeling a system's temporal behaviour in reaction to external stimuli is a fundamental problem in many areas. Pure Machine Learning (ML) approaches often fail in the small sample regime and cannot provide actionable insights beyond predictions. A promising modification has been to incorporate expert domain knowledge into ML models. The application we consider is predicting the patient health status and disease progression over time, where a wealth of domain knowledge is available from pharmacology. Pharmacological models describe the dynamics of carefully-chosen medically meaningful variables in terms of systems of Ordinary Differential Equations (ODEs). However, these models only describe a limited collection of variables, and these variables are often not observable in clinical environments. To close this gap, we propose the latent hybridisation model (LHM) that integrates a system of expert-designed ODEs with machine-learned Neural ODEs to fully describe the dynamics of the system and to link the expert and latent variables to observable quantities. We evaluated LHM on synthetic data as well as real-world intensive care data of COVID-19 patients. LHM consistently outperforms previous works, especially when few training samples are available such as at the beginning of the pandemic.

Author Information

Zhaozhi Qian (University of Cambridge)
William Zame (UCLA)

William Zame is Distinguished Professor of Economics and Mathematics. His interests include Economic Theory, Experimental Economics, Engineering and Mathematics, and Machine Learning and Medicine. He is a Fellow of the Econometric Society and the Society for the Advancement of Economic Theory and a former Fellow of the John Simon Guggenheim Foundation .

Lucas Fleuren (Amsterdam UMC, location VUmc)
Paul Elbers (Amsterdam UMC)
Mihaela van der Schaar (University of Cambridge)

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